as the ratio between perturbation sizes inside
and outside the module to which the perturbed
This measure of the buffering effect indicates
how many times there are more individuals out-
side the module where the perturbation begins
versus inside that module (21). We observed that,
as predicted by theory, modules confine the
spread of the perturbation (Fig. 3). Population
sizes were reduced to a lesser extent in nodes
located outside the module to which the per-
turbed node belongs. On average, this reduc-
tion amounts to 23% (t = 0.87, P = 0.38) when
the local population is separated from the per-
turbed node by a distance of one link and to
46% (t = 3.04, P = 0.002; one-tailed, paired
t test) when separated by a distance of two
links (21) (fig. S20).
At this point, however, we could not be certain
about whether modularity is the network property responsible for this result because our experiment included only one network configuration.
One way to verify that modularity is the driving
factor is to compare the observed results with
those obtained with different assignments of nodes
to modules. We originally assigned nodes to modules
in a way that maximized modularity. We next examined whether any other assignment of nodes
to modules could have returned a similar or even
greater degree of buffering. To do this, we calculated the buffering effects after randomizing the
node-module assignment (21). Our results (Fig.
3) show that assigning nodes to modules in a
way that maximizes modularity results in the
largest buffering effect. We conclude, therefore,
that network modularity buffered the spread
of perturbations in these experiments.
Our experimental result is constrained by network size and configuration, so we next explored
the generality of our results by using a metapopulation model of F. candida in habitat networks.
200 14 JULY 2017 • VOL 357 ISSUE 6347 sciencemag.org SCIENCE
Fig. 2. Module partition and population dynamics in each node. (A) Each
node is identified by a number, and its color indicates the module to which it belongs.
Links between modules are in black, whereas links within a module have the
same color as the nodes from that module. The asterisk indicates the perturbed
node. (B) Time series for each node in one of the perturbed network replicates. Lines
represent the log-transformed number of individuals of each node, counted with the
image processing algorithm. Line colors match the module to which those time
series belong. The shaded area shows the beginning and end of the perturbation. It is
easy to see the perturbed node (5, lower blue line), where individuals were removed
during the perturbation period. A low population size was maintained in node 5
because of immigration from adjacent nodes, and it recovers once the perturbation
comes to an end. (C) Time series for each node in one of the unperturbed network
replicates. Note that there are no extirpations in either the perturbed or unperturbed
network. Final population densities differ among nodes in both (B) and (C).
Fig. 3. Modular networks buffer the spread of perturbations. (A and B) Probability density
distribution of the average buffering values if the assignment of nodes to modules is random. The
thin dashed line (buffering = 1) indicates no effect of modularity, as the decrease in the number of
individuals due to the perturbation would be the same inside and outside the module to which the
perturbed node belongs. The thick dashed line indicates the average observed buffering of the
module assignment maximizing modularity. Panels (A) and (B) correspond to distances from the
perturbed node of one and two links, respectively. We include randomizations only where the number
of nodes inside and outside is the same as in the assignment within the experimental microcosms.